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arXiv · hep-th/0206202

Gravitational instability in higher dimensions

Gary Gibbons·Sean A. Hartnoll
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Abstract

We explore a classical instability of spacetimes of dimension $D>4$. Firstly, we consider static solutions: generalised black holes and brane world metrics. The dangerous mode is a tensor mode on an Einstein base manifold of dimension $D-2$. A criterion for instability is found for the generalised Schwarzschild, AdS-Schwarzschild and topological black hole spacetimes in terms of the Lichnerowicz spectrum on the base manifold. Secondly, we consider perturbations in time-dependent solutions: Generalised dS and AdS. Thirdly we show that, subject to the usual limitations of a linear analysis, any Ricci flat spacetime may be stabilised by embedding into a higher dimensional spacetime with cosmological constant. We apply our results to pure AdS black strings. Finally, we study the stability of higher dimensional ``bubbles of nothing''.

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Gary Gibbons, Sean A. Hartnoll. 2002-07-23. Gravitational instability in higher dimensions. https://doi.org/10.1103/physrevd.66.064024

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